In this paper, we study the Vapnik-Chervonenkis (VC)-dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VCdimension of planar visibility systems is bounded by 23 if the cameras are allowed to be anywhere inside a polygon without holes [1]. Here, we consider the case of exterior visibility, where the cameras lie on a constrained area outside the polygon and have to observe the entire boundary. We present results for the cases of cameras lying on a circle containing the polygon (VC-dimension=2) or lying outside the convex hull of a polygon (VC-dimension= 5). The main result of this paper concerns the 3D case: we prove that the VC-dimension is unbounded if the cameras lie on a sphere containing the polyhedron, hence the term exterior visibility.

Sensing remote, complex and large environments is an important task that arises in diverse applications including planetary exploration, monitoring forest fires and the surveillance of large factories. Currently, automation of such sensing tasks in complex environments is achieved either by deploying many stationary sensors to the environment, or by mounting a sensor on a mobile device and using the device to sense the environment. The

Randomized Pursuit-Evasion with Local Visibility We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G.